st: Fixed-effects estimation with 3000 dummy variables

I have to estimate a model with a very large number of dummy
variables (interaction terms made from some 260 industry dummy
variables and 11 year dummy variables) where I want to control for
establishment level fixed-effects, too. I generated the dummy
variables, and using pooled data without fixed effects, all this is
easily done by using AREG and absorbing the 3000 dummy variables.
Unfortunately, to the best of my knowledge there is no such program
as "XTAREG". I transformed my data by subtracting the mean values
within the industry-year cell, and using these data in a simple OLS
estimation without a constant gives the same results as the models
using AREG (as it should).

Question: Is it correct to use XTREG with these de-meaned data, and
the option FE, to estimate the fixed effects version of the model? Am
I missing something obvious?

(As an aside, I know that I could use XI:XTREG here, but the do-files
will run for many days, and the runs have to be done inside the
Statistical Office for privacy reasons, and the PC is not allowed to
run over the weekend ...)